Solve (sqrt{8}+sqrt{9})*3^7

$$( \sqrt { 8 } + \sqrt { 9 } ) \times 3 ^ { 7 }$$

Evaluate

$$2187\left(2\sqrt{2}+3\right)\approx 12746.77012182$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\left(2\sqrt{2}+\sqrt{9}\right)\times 3^{7}$$

Calculate the square root of 9 and get 3.

$$\left(2\sqrt{2}+3\right)\times 3^{7}$$

Calculate 3 to the power of 7 and get 2187.

$$\left(2\sqrt{2}+3\right)\times 2187$$

Use the distributive property to multiply 2\sqrt{2}+3 by 2187.

$$4374\sqrt{2}+6561$$